How can I make a legend for this plot?

plot([17.85*(2.65*t^2 + 1 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 47 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 97 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 147 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 197 + 3*t)^2/t^2], t = 0 .. 25, labels = ['t', 'x'], labelfont = [Times, 12])

 I got the following figure.

Now I want to put a legend box in this plot for each color line. How can I do it?
 

Could anyone please help me to find the root means of the value of x for different values of k in the range 0.1..0.9  by putting the expression P=0 by using the Newton method? 

Help_Newton_Method.mw

Dear Maple community,

I am facing a little problem verifying a power series solution obtained with Maple since the direct substitution back into the PDEs does not seem to be conclusive because the residual contains the powers of independent variables to almost any order.

Please see the enclosed Maple file with a minimal working example:

Download MinWorkingExa.mw

Thanks a lot in advance for any help or suggestions.

Kind regards,

DDe

Suppose I have an expression like the following:

h(t, x) :=  (m*t^2 + 6*t - 2*x)^2/(36*g*t^2)

I want to calculate multiple values of t in a single expression. Say, for t:= 1,5,10,15,20. I want to evaluate h(t,x) in vector form. so that I can extract for each t. How to write it?

Hello everyone, I am trying to generate a relation for x in terms of lambda by putting my expression (A=0) but do not get the explicit relation. Could anyone please help me generate data points between x=[0..1] and lambda by putting A=0 and then making a polynomial by using the fit curve for x in the term of lambda?

Help_Data_points.mw

How do we define a matrix or a vector of the partial differential operator?
 

How to evaluate the right eigenvector of a given matrix in maple?

How to obtain the commutator table of the infinitesimal generators?
Can we obtain a commutator table by using any inbuild command in pdetools?

I got a plot by following the code in Mpale 2022.
restart;
with(plots);
P2 := plot3d(-t^2 + x, t = 0 .. 20, x = 0 .. 400, labels = ['t', 'x', 'rho'], labelfont = [Times, 15], viewpoint = "circleleft", colorscheme = ["ygradient", ["Green", "Purple", "Blue", "Red", "BlueViolet"]]);
plotsetup(ps, plotoutput = "P2");
print(P2);

Then I tried the following code for the overleaf. However, I did not get the desired result.

\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{epsfig}

\begin{document}
Plot obtained from Maple 2022. \\

\includegraphics[width=0.9\textwidth]{P2.eps}
\end{document}

plotting_file.pdf

Any help is highly appreciated.
Thanks
Deb

I am wondering why Maple simplifies (x^(1/3))^3 to x ,  but not (x^3)^(1/3) .
I even tried the surd function. I believe the surd function is for real number arguments, so it should simplify to x.

Download inverse1.mw

I asked maple to solve a basic log inequality.
;

This is what happened.

Here is a link to the document to replicate this behavior.

log_inequality.mw

I know there is a solution , if you look at the [graph](https://www.desmos.com/calculator/3n7uzwrak4).

I also tried fsolve, but you have to narrow down the solution interval to look for a solution, and use an equality instead of an inequality.

For t not equal to nT,   

dS/dt = delta- mu*S+ omega*V; 

 dV/dt = -(omega+mu)*V

For t=nT, 

 S(nT⁺)=(1-gamma) S(nT);

V(nT⁺)=V(nT)+ gamma* S(nT),

with the initial conditions  S(0⁺)=s₀

V(0⁺)=v₀

    how to plot the graph with this system of equations,impulsive points and initial conditions  

i am facing problem while solving differential equation in loops where conditons are given also in loops. the particular problem occurs while solving Differential equation involving He's Homotopy purturbation method

How  to make the integration 

into the following form:

Thanks in advance,Q1.mw

IsFrobeniusGroup(SmallGroup(20, 3)) will get true, but IsFrobeniusPermGroup(SmallGroup(20, 3)) will get false. What happen? As the documentation, it will get same result:

The two definitions are equivalent in the following sense.  If G is a Frobenius permutation group, then G is Frobenius as an abstract group